It is not possible for a buyer to meet a seller directly. Each investor must have a broker and when you want to sell or buy a stock the broker will place your order in the exchange computer. When you get a seller or a buyer the exchange will tell your broker and finally you will be informed by him. You cannot deal directly with the exchange yourself. Nor can you meet the person that is buying your stock.
Apart from facilitating the buy-sell process the stock exchange offer several advantages.
1. You do not have to go around looking for people to buy shares. Also even though some companies sell stocks over the counter this is a daunting task and this can be done using a stock exchange in minutes.
2. The stock exchange protect the investors in that you are certain to get a share when you buy and to get your money when you sell. You also have consumer protection institutions that can initiate actions if your rights have been infringed.
3. Companies that are listed on the exchange have to abide to some rules. They need to have a certain market capitalisation, they need to follow accounting standards, they need to issue financial reports every quarter among others, their shares have to be above a certain value, etc. As you can see, if you are investing in a company listed on an exchange you are sure that the company is secure.
4. Companies must get shareholders agreement before going ahead with some plans such as raising the number of shares, mergers and acquisitions, etc.
5. Companies listed on a stock exchange must a board of directors that are independent and capable of doing their jobs. At least in theory.
As you can see trading on the stock exchange offer some advantages. Even though when trading you have to pay some fees, i sincerely believe that the advantages far outweigh the disadvantages. In fact if you are buying for the long term the gain on the long term will be far greater than the fee.
So guys be safe and trade on an exchange.